Logit-Normal模型的MCEM算法参数估计

Parameter Estimation of MCEM Algorithm Based on Logit-Normal Model

EM算法主要被用来处理由于数据缺损等原因导致的不完备数据情形下的参数估计问题.本文在简单介绍EM算法的基础上,又针对EM算法的E步中积分无法计算甚至表达式难以给出的情况,讨论了Monte Carlo EM(MCEM)算法,MCEM算法利用Monte Carlo模拟有效估计出E步中的积分,显著提高了实用性.最后研究了MCEM算法在Logit-Normal模型中的应用,根据Metropolis-Hastings(MH)抽样近似得到积分并通过迭代估计出参数值.

Expectation-Maximization(EM)algorithm is mainly used to solve the problems of parameter estimation in the case of incomplete data due to data missing.Based on a brief introduction to the EM algorithm,our paper discusses the Monte Carlo EM(MCEM)algorithm aimed at the inability to calculate the integral of the E step.The MCEM algorithm uses Monte Carlo simulation to effectively estimate the integral in the E step,which significantly improves the practicability of the EM algorithm.Finally,we apply MCEM algorithm to the simple LogitNormal model and obtain the integral by Metropolis-Hastings(MH)sampling.